CHAPTER 5. EMPIRICAL RESULTS
5.1 The Efficiency Score of Social Security
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立 政 治 大 學
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CHAPTER 5. EMPIRICAL RESULTS
Before estimating the Tobit model, two efficiency scores of social security in 31 provinces have to be measured by the DEA approach in the first section of this chapter. Using these two efficiency scores as dependent variables, four specifications of the Tobit model are estimated and analyzed in the second section of this section.
The last section in this chapter is about the regional-specific and time-specific effects in the Tobit model.
5.1 The Efficiency Score of Social Security
The efficiency scores of CRTE and VRTE are calculated based upon equations (4.1) and (4.2), respectively. The inputs and outputs which this study uses to illustrate the efficiency of social security are introduced in section 4.3.1. It is worth noting that this study runs the DEA model with all data, which are 279 observations,32 to
represent the characteristics of panel data.33 The efficiency scores of social security in selected years are presented in Table 8.
Table 8 shows that efficiency scores draw from CRTE are quite different from those of VRTE. As a whole, the efficiency scores of VRTE are higher than those of
CRTE and more provinces have highest efficiency score, which is one, under the
assumption of VRS.34 The assumption of VRS results in the limitation of non parametric mathematical program much looser, so the efficiency scores under the assumption of VRS are higher than those under the assumption of CRS. In addition,
32 279 observations are the data of 31 provinces in nine years.
33 This study runs the DEA model twice, one is under the assumption of CRS (CCR model), and the other is under the assumption of VRS (BCC model).
34 In 279 observations, there are 5 data which achieve the highest efficiency score under the
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Table 8: The Efficiency Score of Social Security in Selected Years
Regions CRTE VRTE Difference1
Source: Various years of the China Statistical Yearbook.
Note: 1. The difference between the scores of efficiency in 2009 and 2001 in the same region.
2. The regions are similarly categorized by the area dummy variables.
3. Numbers, ★, and shadows in parentheses represent rankings of top three provinces with larger increase, the highest efficiency scores, and the lowest efficiency scores and bottom three provinces with larger decrease.
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the average scores of CRTE show an upward trend over time, but the average scores of VRTE show a downward trend over time. Meanwhile, the increasing magnitude of
CRTE is larger than VRTE.
Under the assumption of CRS, there is one province with CRTE=1 in 2001, which is Shanghai, implying the highest efficiency score. However, the numbers of province with the highest efficiency score increase to two in 2009, which are Beijing and Shanghai. However, the provinces with the lowest efficiency score, which is 0.1, are Hunan, Sichuan, and Yunnan in 2001. In 2009, Qinghai has the lowest efficiency score, which is 0.19. During the research period, every province has improved their efficiency of social security. The top three provinces with larger increase of CRTE are Zhejiang, Jiangsu, Guangdong, which have the same scores, and Fujian, accordingly.
These provinces all gather in the eastern area.
With regard to VRTE, more provinces have the highest efficiency scores under the assumption of VRS than under the assumption of CRS. Shanghai is the only one province with the highest efficiency score in 2001, but in 2009, there are three provinces with the highest efficiency score, which are Beijing, Shanghai, and
Zhejiang. However, the provinces with the lowest efficiency score, which is 0.52, are Hunan and Qinghai in 2001. In 2009, Qinghai still has the lowest efficiency score, which is 0.49. In addition, during 2001 to 2009, only ten provinces have increased or retained their efficiency scores. The top three provinces with larger increase of VRTE are Zhejiang, Fujian, and Guangdong, accordingly. These provinces also gather in the eastern area. Conversely, the bottom three provinces with larger decrease of VRTE are Tibet, Guangxi, and Gansu, by order. These provinces all gather in the western area.
Moreover, according to Table 8, the provinces in all areas have improved their
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worth noting that the largest increase of CRTE appears in the eastern area, which is 0.25. The provinces that are in the eastern area have improved their efficiency of social security obviously under the assumption of CRS. However, this phenomenon shows completely converse under the assumption of VRS. Only the provinces in the eastern area have improved their efficiency of social security under the assumption of VRS. The remaining provinces in those three areas have suffered the decrease of efficiency. The western area has the largest decrease of VRTE, which is 0.08. This conclusion shows that there is still a serious regional inequality in China. The higher efficiency scores always appear in the eastern area, no matter under the assumption which CRS or VRS, but the lower efficiency scores gather in the both central and western areas, no matter under the assumption which CRS or VRS.
Due to the different scenarios observed based on CRTE and VRTE, this study estimates two specifications of the Tobit model. One uses CRTE and the other one uses VRTE as dependent variables, for confirming the robustness of findings
regarding the influence of fiscal decentralization on the efficiency of social security in China.